# Tagged Questions

Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

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### How can I use the time-frequency uncertainty principle?

I have a signal composed of the summation of a set of sine waves of different frequencies. The amplitude of these sub-signals can change so many times a second. I have been told that, if I want to ...
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### How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
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### Analysing the modes of a signal with Laplace transform

If I have a linear dynamical system (assume continuous time for the time being) I can create the transfer function, let's say: $$\frac{1}{(s+a_1)(s+a_2)}$$ and the pole-zero map (this one is for e.g. ...
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### Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car. In a Kalman filter the matrix ...
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### Unknown normalization

I am trying to do BPP imaging and have been trying to replicate the algorithm in "Photoplethysmographic imaging of high spatial resolution" however I've ran into a problem. They say they normalize ...
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### Using 2D Parseval-Plancheler theorem to solve an equation

In the context of a digital communications problem I have to solve the following equation with respect to $\tilde{\tau}$: \begin{eqnarray*} &&Im\Big\{\Big(\int\limits_0^{T_0}r^{*}(t)g(t-\tilde{...
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### Quality of a signal (cascaded)

This question extends my previous one Quality of a signal to the case of two cascaded signals. We have a signal x(t) that is transformed (T1) into v(t) that is transformed (T2) into y(t). We want to ...
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### Wavelet or FFT for Transient signal analysis?

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frenquency domain. On the other hand I ...
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### Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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### need help with following butterworth filter unit sample response.

I have a problem for you. Can anyone help me to solve this. A system is represented by a0y(n)+a1y(n-1)+a2y(n-2)+a3y(n-3)=b0x(n)+b1x(n-1)+b2x(n-2)+b3x(n-3) B= [b0, b1 , b2 , b3 ]= [0.3151*10-3 0....
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### FFT butterfly diagram

I got confused in the FFT butterfly diagram. Can someone please help me understand it? If I have the vector $x = (-3, -2, -1, 0, 1, 2, 3, 4)$, and I want to apply FFT to it using the Butterfly ...
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### DFT of a sequence while ignoring some of its elements

I sample a signal at a certain frequency for a finite amount of time to get a sequence $$(x_n)_{n=1}^N = (x_1, x_2, ... , x_N)$$ with the intention of analyzing its power spectral density by ...
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### Convolution: $f (-)*g = g(-)* f$ does this mean both $f$ and $g$ have to be even functions?

Assuming $f$ and $g$ are different functions, does $f (-)*g = g(-)* f$ mean both $f$ and $g$ have to be even functions? In fact, this is equivalent to $f\star g = g \star f$ (i.e., cross-correlation ...
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### Has the theoretical explanation of Compressed Sensing been simplified since 2005/2006?

Is the theoretical explanation of compressed sensing given in the Candes, Romberg, and Tao papers from 2005 / 2006 still the simplest and most clear explanation available? Are these original papers ...
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### How do I exactly project a vector onto a subspace?

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am not ...
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### Equation for a sinusoidal wave with changing frequency

I would like to find a sinusoidal wave whose period or frequency change to half (or double) with every step, someting like this But I cant find the precise coefficients for the period to decrease (...
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### What is a cardinal basis spline?

Wikipedia says: the normalized cardinal B-splines tend to the Gaussian function and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says: The basis splines Bn are shown ... ...